The equation of a circle $C$ is $(x+4)^{2}+(y+5)^{2} = 1$. What are its center $(h, k)$ and its radius $r$ ?
The equation of a circle with center $(h, k)$ and radius $r$ is $(x - h)^2 + (y - k)^2 = r^2$ We can rewrite the given equation as $(x - (-4))^2 + (y - (-5))^2 = 1^2$ Thus, $(h, k) = (-4, -5)$ and $r = 1$.